[SOLVED] Matrix problem, a bit clueless

Find the reduced row equivalent to , where . I won't show my calculus but I found to be .
Now the problem states : Find all the such that . So I had the following system I think this implies infinity solutions (but I'm not sure) so I thought I made an error. So I restarted the calculus of without following what I've done for my first try and I found out that . Is that possible?
The problem says "the reduced row equivalent to " so I made at least an error... And also if this calculus was right, I would have the same problem solving for , and . Please help me!

Find the reduced row equivalent to , where . I won't show my calculus but I found to be .
Now the problem states : Find all the such that . So I had the following system I think this implies infinity solutions (but I'm not sure) so I thought I made an error. So I restarted the calculus of without following what I've done for my first try and I found out that . Is that possible?
The problem says "the reduced row equivalent to " so I made at least an error... And also if this calculus was right, I would have the same problem solving for , and . Please help me!

both are the same. the first answer you got is in the appropriate form

there is no leading 1 in the third column, so the variable for that column, namely , is your parameter. you will have an infinite number of solutions based on its value. (i assume you reduced the matrix properly)

so you have:

so that

and that's it. you get a new solution for each t, so that's all solutions

And why not my 2nd answer? Isn't it row reduced (the problem didn't say "echelon")?
And for

there is no leading 1 in the third column, so the variable for that column, namely , is your parameter.

so it seems I had to row reduce it echelonly because my third row could have been the second row, for example. Unless it wouldn't be under an appropriate form.

I cannot understand your difficulty.

The problem states that there is only one row reduced matrix equivalent to and I found out at least 2. But Jhevon told me that one is not under the appropriate form, so it seems there's only one of them, now I understand it.
I was also doubting about an infinity of vectors that satisfy because the next question ask "check out that for all the X found, ." I thought there was a finite number of them, but it seems that it's not necessary.